Diary - December 2006

John Baez

Blowing down from the Northwest through the Rocky Mountains,
it slammed into the Midwest from
Michigan all the way down to Texas, where some roads were covered
with ice and up to 7 inches of snow. More than 400 hundred flights
were canceled at Chicago's O'Hare Airport, and 200 at Dallas-Forth Worth.
Further north, some areas are getting 2 inches of snow per hour!
Tonight fierce winds will hit New England.

Meanwhile it's chilly down here - chilly for Southern California, anyway.
Not really cold at all.
But last night, I curled up in bed and read about the end of the last Ice Age.
I find this tremendously romantic, because it paints a portrait of a land
recognizably like our own, but strangely different:

Evelyn C. Pielou,
After the Ice Age: the Return of Life to Glaciated North America,
U. Chicago Press, Chicago, 1991.

Written by one of the founders of mathematical ecology, it reads
like a novel, with nary an equation.

Let me set the stage with some dates. The last Ice Age - the Wisconsin
glaciation, began in about 70,000 BC. The oldest known cave
paintings date back to 32,000 BC. The glaciers reached their
maximum extent about 18,000 BC, with ice sheets down to what
are now the Great Lakes. In places the ice was over a mile thick!
That's 1.6 kilometers for you metric folks.

Then it started warming up. By 16,000 BC people started cultivating
plants and herding animals. The first known people in the Americas
date back to about 11,500 BC - they're called the
Clovis
culture.
By about 10,000 BC the Ice Age had ended.
The first cities in the Old World date to around 7,500 BC; cities
in the Americas seem to come much later.

At the time of maximum glaciation, there were three main refuges for
life in North America. Biologists call such things "glacial
refugia". The first was all the land south of the glaciers,
including an "ice-free corridor" just east of the Rocky
Mountains. The second was Beringia, a huge region
made of what's now Yukon and Alaska, together with eastern Siberia.
As you can see, the ocean was lower when more water was frozen up in
glacier and the ice caps:

The third was the coastal plain region of eastern America, which is
now submerged to form the continental shelf off the coast of New
England and Canada.

Besides these big refugia, there were also smaller coastal refugia and
nunataks -
mountains too high for the glaciers to cover them!

What was life like south of the ice sheets around 16,000 BC? In the
eastern half of the continent there was tundra and spruce forest.
Further west it was drier, except for a belt that got runoff from
melting glaciers. West of what is now Minnesota it was too dry for
forests - just grasslands. And where the Great Plains now reign
supreme, there was a huge area of sand dunes!

There were many large mammals. Largest of all were the American
mastodon and four species of mammoths, only two of which survived
to the end of the ice age: the woolly mammoth in
the tundra of Beringia, and the much larger Jefferson's
mammoth in the central plains and the west. Both these went
extinct around 9,000 BC, perhaps killed off by humans.
Bones from butchered mammoths have been found with Clovis spear points in
Wyoming
and South Dakota.

There was also the
Mexican horse and
western
camel, both now extinct. Recently people have found spearheads dating
back to 8,300 BC bearing protein residue from the
Mexican horse! Indeed, this horse may have been hunted into extinction.
Early Americans also hunted the western camel in Wyoming,
as recently as 8,000 BC, which is around when they died out.

Caribou and
tundra muskox
ranged far further south than they do today.
The tundra muskox probably crossed into Beringia around 90,000 BC.
There was also a species of
woodland
muskox, now extinct. The elk, white-tailed
deer, mule deer, bison and bighorn sheep that we know
today were already widespread.
But there were apparently no moose, except in Beringia.

But I know what you're wondering: what about carnivores?

The familiar cougars, bobcats and black bear were already here.
Timber wolves were present but uncommon. Grizzly bears reached
midlatitude America only after the ice sheets began to melt. But
there was also the dire
wolf, similar to the modern wolf
but bigger and stronger. There was the sabertooth, about the size of a lion,
with incredible teeth. There was its smaller relative, the
scimatar cat...
and the American lion,
and the American cheetah!
All these are gone.

And then, there was the giant
short face bear. This was the most powerful predator
of the lot: a flesh-eater with powerful jaws, and probably quick on its
feet, able to run down prey.
It stood 1.6 meters (5.5 feet) at the shoulder. It
weighed about 900 kilograms (almost a ton).
You would not want to meet one of these:

I recently mentioned the rise of relationships conducted over the phone. But did you know that over a
million people live part of their lives in a 3d virtual reality
environment called Second Life? This is
run on a computer network called the Grid:
hundreds and hundreds of servers, each of which simulates 64,000 square
meters of land. People rent this land, starting at $5 per month for
the bare minimum area, 512 square meters. There is also an initial
fee, which for this minimum unit is between $10 and $25. But, many
people own whole islands and pay $3,000 a year!

Some companies are starting to hold conferences on the grid.
They've got their own antique
bookstore in there:

Thanks, that's interesting. New Scientist (which, honestly, is
interesting quite often, when they stay away from magic anti-gravity
devices) had a story a few months ago on the growing economies of online
worlds, and the growing presence of more serious crime now that virtual
money can be exchanged for real money in some of them.

None of this makes me believe in an imminent technological singularity,
though, unless you define it in the "weak" sense of "strange
things
happening that almost nobody predicted", in which case we've had lots of
them already. What I'm extremely sceptical about is the idea that we're
on the verge of writing self-improving software, which will inspect
itself and modify itself (and eventually its physical substrate) in ways
that will lead to an exponential increase in its speed, efficiency and
capabilities; in other words, we'll just "light the fuse"
and then some
spectacular new form of intelligence will arise. We might be on the
verge of various stupid mistakes that wreak havoc on the internet, and
within a few decades of even stupider mistakes that could wreak havoc on
the real world, but I don't count either kind of disaster as a
singularity ... it's only a singularity if the grey goo starts talking to
you.

This doesn't really refute anything singular-esque, but you might be
amused to know that it took the people responsible for Java eight years
to regain the ability to draw circles; this used to work fine in their
early version, but then they added lots of fancy complications to their
graphics routines, and circles proved to be just too hard to get right:

I could try to explain what I "really meant",
but I don't think really meant anything - I was just in awe of this
Second Life stuff,
a kind of technofantasy coming true before I expected it, without me even
noticing.

Last night I got a nasty stomach flu, which has now died down to a fever
and general weakness and malaise. Tomorrow I fly for Stanford, where I'm giving
a math talk
the next day, so I'd better go to bed early now. After my talk I'll go out
to dinner with the mathematicians and also
Eric
Drexler - the nanotech guru, who works at the
same company as my pal
Bruce Smith. Eric's wife
Rosa Wang
will also be there. I've never met them. It should be interesting.

It's indeed an interesting piece, in part because it clarifies the
feeling I had when I said
"You can tell we're heading
for a technological singularity, when weird stuff like this is going on
and lots of people don't even hear about it!". It suggests
that people have been feeling this a bit for a long time, and could keep
on feeling it for a long time, without there necessarily being a moment
at which the intensity of new weirdness becomes infinite: a moment
of complete rupture, or Rapture.

To be good scientists we really should
save the term "singularity" for
a point at which something become infinite. Kelly wisely points out
that there doesn't need to be a moment like this coming up, even if
change is growing faster, and the rate of change of change is growing
faster, and so on. Exponential growth will suffice!

There's a lot more to say about this - stuff about phase transitions
and the like - but I'm too tired right now.

(By the way, I'm starting to quote more emails in my diary.
If you're considering mailing me, don't be afraid that
I'll just stick your email into your diary. If I want to do it,
I will ask permission first.)

My talk at Stanford
went okay, but certainly didn't leave them cheering in
the aisles. The dinner was small, with just Rafe Mazzeo, Eric
Drexler and Rosa Wang. A great conversation, and sometime soon I
should try to write down a few things I learned, before I forget them
all - I've already forgotten half.

I hope this talks about the
Clovis culture.
These are the
first people known for sure to have entered the Americas, though
there are fascinating theories of still earlier New World cultures, based on rather
skimpy
evidence. They get their name from
a beautiful style of rock spear point they used, the
Clovis point.
It's believed they crossed Beringia around 12,500 BP (Before Present)
and then came south through the Rocky Mountain ice-free corridor.
Some say they're to blame for a wave of extinctions among mammals in
the New World around this time - this is called the
"Pleistocene overkill hypothesis". Indeed, the above
picture is from:

On October 7th and
October 9th I discussed
the Paleocene-Eocene Thermal Maximum. This was a sudden spike in
temperature 55 million years ago, in which global temperatures shot up
5-8° C for a few thousand years. You can see it here - it's labelled
"PETM":

I mentioned some new evidence that the the PETM
was due to a sudden release of greenhouse gases - in particular, a
"methane burp" where methyl hydrates on the sea floor suddenly
got loose into the atmosphere. It seems worth studying, since it may be
the closest natural analogue of the burst of global warming we are suffering now!

My friend Bruce Smith subscribes to lots of science magazines, so I happened
to bump into some articles that are relevant - especially the second
one here:

Declining atmospheric CO2 has long ben envisaged as a culprit
for the past 55 million years of cooling climate, and the consequent
transition from an ice-free world to one with large ice sheets on
Greenland and a
frozen Arctic, as well as with a deep-frozen Antarctica. Indeed,
reconstructions of past atmospheric CO2 concentrations,
based on isotopic markers from marine algae, show a dramatic drop in
atmospheric CO2 between about 45 million and 25 million
years ago that corresponds quite well to the onset of major global
cooling. However, although the onst of glaciation and sea ice
in Antarctica about 43 million years ago matched the onset of
global cooling and CO2 decline, the Artic seemed
to march to a different drummer. Arctic cooling [...] seemed to
hold off for tens of millions of years, until about 2-3 million
years ago, when pebbles carried by icebergs first appeared in
North Atlantic sediments.

[...]

The puzzle is solved nicely with the new record reported by Moran
et al, which shows Arctic ice developed much earlier than
previous developed. Pebbles carried to the middle of the Arctic
basis by icebergs appear by 45 million years ago, about the
same time as around Antarctica.

Sluijs et al report that 55 million years ago Arctic
summertime surface-ocean temperatures were as high as 18° C.
Such temperatures are comparable to those of the modern summer
ocean on the French coast at Brittany (where hardy souls even go
swimming). More importantly, climate models for
55 million years ago don't even come close to simulating such
warm waters, even when reflective ice sheets are left out and
atmospheric CO2 levels are pumped up to 2,000
parts per million - nearly ten times the levels before
the Industrial Revolution. [...]

Slujis et al also provide intriguing results
for a dramatic burst of intense warming - the
Palaeocene-Eocene Thermal Maximum - that occurred
55 million years ago. This 'Palaeocene supergreenhouse'
is believed to have been caused by a massive release of carbon to
the oceans and atomosphere, either from methane present in deep-sea
sediments or as organic carbon vaporized by volcanism during the
opening of the North Atlantic Ocean. In either case, the
extra CO2 in the atmosphere increased the
greenhouse effect and warmed tropical temperatures by
4-5° C. Sluijs et al show that Arctic
temperatures also soared, rising from 18° C to 23° C.

In fact, Sluijs et al looked at sediments in a formation
called the Lomanosov Ridge in the center of the Arctic Ocean.
They could tell which sediments formed during the Paleocene-Eocene
Thermal Maximum by seeing an abundance of fossils from tiny sea
creatures that normally like subtropical oceans. In the organic
material in these sediments, they saw a 2.5% decrease in
carbon-13 concentrations at the time of the PETM.
Since carbon-13 is a radioactive isotope
made when carbon dioxide in the atmosphere gets zapped by cosmic rays,
this suggests that a bunch of new carbon from deep below
was released at this time! The obvious candidate is a methane
burp.

How much is "a bunch" of carbon?
At least 1.5 × 1015 kilograms, or in other
words, 1.5 trillion tons! This is as
much as all the current and expected carbon released
by our use of fossil fuels!

So, from this ancient history, we may get some idea of the future effects
of our current fossil fuel usage.

Of the four carrier groups that were last month (November 2006) in
the Persian Gulf and nearby waters:
Enterprise, Eisenhower, Iwo Jima, and Boxer
two have returned home:
Iwo Jima arrived in Norfolk today (6 December 2006)
and
Enterprise is also home.
From an article dated 2 December 2006 on the web at
http://www.strategypage.com/dls/articles/2006122232136.asp:
"... The American carrier USS Enterprise recently returned
from 30 weeks at sea. It was an unusual voyage, ...
seeing combat in both Iraq and Afghanistan.
Enterprise aircraft only dropped four bombs in Iraq,
while dropping 133 in Afghanistan ...
In Iraq, aircraft spent nearly all their time doing recon,
or electronic warfare (zapping roadside bomb detonators,
or searching for enemy transmissions.)
One unusual aspect of this voyage was that no one was killed.
Normally, there is at least one death on a deployment that long. ...".
So, it seems that the 4-carrier deployment did not result in
any major attack related to Iraq/Syria/Iran,
which is consistent with the position of the USA Baker-Hamilton group
as described by a DEBKA article at
http://www.debka.com/headline.php?hid=3601
which said about that report:
"... Four significant changes are indicated:
1. The US finds itself unable to prevent or respond to an Iranian nuclear
attack on Israel, as incoming defense secretary Robert Gates stated bluntly
in the Senate committee hearing Tuesday.
2. American forces will be gone from Iraq in just over a year.
3. Washington will soon embark on a fresh Israeli-Palestinian peace initiative.
4. Direct US-Iran, US-Syria talks are in the offing. ...".
I hope that the fact that there were no deaths during the Enterprise
deployment is a good omen.
Tony

My friend Bruce Smith has a great way of clarifying hard puzzles by
simple, clear reasoning. In our last few conversations he
told me his ideas on the Fermi paradox,
and, later, on the
the Gaia hypothesis.

I last talked about the Fermi paradox in my October 27th
entry. Bruce's main idea here is that there's
so much uncertainty in all the variables in the Drake equation that we might as well
just admit the possibility that our Earth is the first
civilization in our past lightcone to be able to send signals for
really long distances at the speed of light (radio, television).
Given this, we can put an upper bound on the density of such civilizations.
There are a lot of interesting calculations to be done here - but
not today.

What about the
Gaia
Hypothesis? This says that life on Earth serves to
regulate the Earth's temperature, rainfall, and the concentration of
various gases in the atmosphere and minerals in the ocean - keeping them
all at conditions suitable for life. In short, life serves
as a homeostatic
mechanism, like a thermostat keeps your house from getting too warm
or cold.

This hypothesis might explain, for example,
why the Earth's temperature has not increased since life started.
In 3.5 billion years the Sun will become 40% brighter than today -
hot enough for the Earth's oceans to evaporate. But in fact,
the Sun is getting bigger and brighter already, and now it puts
out 25% or 30% more light than it did when life began. However -
the Earth hasn't gotten any hotter during this time! Could life
on Earth be regulating the temperature somehow?

It's a nice thought.
The first problem is: how could life act to maintain
optimal conditions in the Earth's overall environment?

To tackle this problem, the original proponent
of the Gaia Hypothesis,
James Lovelock,
proposed a simple toy model
called Daisyworld.
In this model, white daisies thrive when it gets hot, while black
daisies thrive when it gets cold. So, when it gets hot, white daisies
spread, which bounce more sunlight back into the atmosphere and cool
things down. When it gets cold, black daisies spread, which retain more
energy from the sun and warm things up! So, they serve as a kind
of thermostat.

This is fine as far as it goes, but one can imagine another world
where black daisies thrive when it gets hot, while white ones thrive
when it gets cold! Here any heating or cooling would get amplified
by the presence of life, instead of counteracted.

Of course it's better for everyone if life serves to counteract
disturbances in the environment rather than amplify them. But this
isn't enough to justify the Gaia Hypothesis.
Just because homeostasis is good for life as a whole doesn't
mean any individual organism will do its part to create homeostasis -
unless somehow it confers a significant competitive advantage to that
particular organism. (We're being hard-headed evolutionary biologists
here, not mystics.)

In short: what selection pressure could push organisms to maintain
optimal conditions in the Earth's overall environment?

Bruce provided a simple possible answer. Let's consider the example
of temperature again. It's easy to see how
each individual organism gets an advantage from cooling itself
down when it gets too hot, or warming itself up when it gets too
hot. What's a good way to cool down? By being white, and reflecting
sunlight! What's a good way to warm up? By being black, and absorbing
it! So, it might really be to the daisy's individual advantage
to be white if it's too hot, or black if it's too cold.

There are lots of questions left, of course. First of all, there's
the question of whether this really happens. When Bruce told me his
idea, I joked "So that's why polar bears are black!"
In fact, many Arctic creatures are white. Clearly the advantage of being well
hidden in the snow outweighs the advantage of absorbing some extra sunshine
during the day. And, as Bruce pointed out, one must also consider
nighttime: being good at absorbing radiation of a certain frequency in
the day also means being good at emitting it at night. (But, we can
easily imagine a creature that's good at absorbing visible light and
bad at emitting infrared - this would be the best way to keep warm during
both the day and night.)

Actually, if we're serious about looking for homeostatic mechanisms, we
should look not in the Arctic - the color of polar bears couldn't possibly
have much of an effect on global climate - but in forests and grasslands.
Plants cover large portions of the Earth, and they could have
a significant moderating effect on the climate. In fact it's
known
that they do! One can imagine survival-of-the-fittest reasons why
each individual tree would do well to regulate the temperature in its
neighborhood; then, when you have a whole forest of them, the effect
gets dramatically multiplied.

It would be interesting to see if this kind of effect can really
justify the Gaia hypothesis. I should read these:

Today I drove James Dolan to the airport - he's spending a
few weeks back home in Long Island before going to the
Fields Institute workshop I'm helping organize on
Higher Categories and their Applications.
En route we talked about categorifying quantum groups - a bunch
of ideas have suddenly fallen into place, so I'll have to write
up something soon.

Before dropping Jim off at the airport, we stopped by
Chris Lee's house, since Chris had a spare laptop for Jim
to use. Now I'm back at Chris' house; I'll spend the night
here and pick up Lisa at the airport next morning... she's coming
back from Shanghai!

As usual when I visit Chris and his wife Menakshee, I've been bombarded
with lots of interesting books and new ideas. This time I'll try to list
some before I forget.

William Poundstone, Fortune's Formula: The Untold Story of the
Scientific Betting System that Beat the Casinos and Wall Street,
Farrar, Strauss and Giroux, New York, 2005.

Packed with rollicking tales of horse-racing, blackjack,
and insider trading, this is fundamentally
the story of Claude Shannon's development of information
theory - and how he and his sidekick John Kelly Jr. used it to make money
in casinos and Wall Street. I'd known about Shannon's
work on entropy and information... but not that he beat
99.9% of mutual fund managers, making an average compound return
of 28% from when he got rolling to 1986 - as compared to 27% for
Warren Buffett!

I like this equation of Kelly's:

Gmax = S

Here Gmax is the maximum expected
growth of a gambler's money, while S is the amount of
"inside information" the gambler has - information
that other people don't have.

Gmax is measured logarithmically: let me explain
with an example. Suppose the gambler has a strategy that on
average allows him to multiply his money by a factor of 8.
Then his Gmax is defined to be

log2(8) = 3

We use base 2 here for a simple reason: we measure S, the
amount of inside information, in bits!

Kelly's equation

Gmax = S

implies that if a gambler's S is 3, his Gmax is also 3.
So, if a gambler receives three bits of information,
he can find some trick which on average multiplies his money by 23
= 8. Here the "average" is a geometric mean, not an arithmetic
mean.

To get a feeling for why Kelly's theorem is true, it's best to start
with the simplest example. If R = 1, then Gmax = 1 =
log2 2. So,
if a gambler receives one bit of inside information,
he can double his money!

This sounds amazing, but it's also obvious. Suppose
you have one bit of inside information: whether a flipped coin will
land heads up or tails up. Then you can make a bet with
someone where they give you $1,000,000 if you guess the flip
correctly, and you give them $1,000,000 if you guess wrong.
This is a fair bet, so they will accept. That is, they'll
think it's fair if they don't know you have
your inside information!
Since you do have this information, you'll win the bet, and
double your money on this coin flip.

I like this relation between information theory and gambling,
in part because one stream of Bayesian probability theory says probabilities
are subjectively defined in terms of what bets you would accept.
This is justified by something called the
Dutch book argument.

So, there's a deep relation between gambling and probability -
no news here, really. But, there's also a
deep
relation between probability and information theory, discovered
by Shannon. Briefly, it goes like this:
the information you obtain by learning the value of a
random variable is

S = - ∑i pi log2 pi

where the sum is taken over the possible values of this random variable
and pi is the probability that it takes the ith value.
So, for example, if you flip a fair coin, where p1 =
p2 = 1/2, the information you get by looking at it is

-[1/2 log2 (1/2) + 1/2 log2 (1/2)] = 1

One bit!

So: gambling is related to probability, and probability is related to
information. Kelly's result closes the circle by providing a
direct relation between gambling and information!

But, apparently some of Kelly's ideas are still
controversial in the world of economics and stock trading.
I'll have to read Poundstone's book to learn why.

Next:

Dmitry Nurminsky, Selective Sweep, Kluwer, New York, 2005.

I may never read this but it's about a cool idea. Suppose one organism gets a
mutation that confers it a competitive advantage. Then it will have lots of
descendants, so this mutation will spread... along with other mutant
genes this organism just happens to have.
The other mutations "ride the coat-tails" of the advantageous
one and sweep across the population - this is
"selective
sweep". This has been seen in nature, along with lots of more
subtle effects.

Right now Chris is trying to understand natural selection from an
information-theoretic standpoint. At what rate is information passed
from the environment to the genome by the process of natural
selection? How do we define the concepts here precisely enough so we
can actually measure this information flow?

Chris pointed out an interesting analogy between natural selection
and Bayesian
inference.

The analogy is mathematically precise, and fascinating. In rough
terms, it says that the process of natural selection resembles the
process of Bayesian inference. A population of organisms can be
thought of as having various "hypotheses" about how to
survive - each hypothesis corresponding to a different allele. (Roughly, an
allele is one of several alternative versions of a gene.) In each
successive generation, the process of natural selection modifies the
proportion of organisms having each hypothesis, according to Bayes'
law!

Now let's be more precise:

Bayes'
law says if we start with a "prior probability" for some
hypothesis to be true, divide it by the probability that some
observation is made, then multiply by the "conditional
probability" that this observation will be made given that the
hypothesis is true, we'll get the "posterior probability"
that the hypothesis is true given that the observation is made.

Formally, the exact same equation shows up in population genetics! In
fact, Chris showed it to me - it's equation 9.2 on page 30 of this
book:

R. Bürger, The Mathematical Theory of Selection,
Recombination and Mutation, section I.9: Selection at a single
locus, Wiley, 2000.

But, now all the terms in the equation have different meanings!

Now, instead of a "prior probability" for a hypothesis to be
true, we have the frequency of occurence of some allele in some
generation of a population. Instead of the probability that we make
some observation, we have the expected number of offspring of an
organism. Instead of the "conditional probability" of making
the observation, we have the expected number of offspring of an
organism given that it has this allele. And, instead of the
"posterior probability" of our hypothesis, we have the
frequency of occurence of that allele in the next generation.

(Here we are assuming, for simplicity, an asexually reproducing
"haploid" population - that is, one with just a single set of
chromosomes.)

This is a great idea - Chris felt sure someone must have already had
it. A natural context would be research on genetic
programming, a machine learning technique that uses an
evolutionary algorithm to optimize a population of computer programs
according to a fitness landscape determined by their ability to
perform a given task. Since there has also been a lot of work on
Bayesian approaches to machine learning, surely someone has noticed
their mathematical relationship?

After a day of talking (and working - it took quite a while to
write up the above stuff), we ate out at
M & M Soul Food
in a jazzy neighborhood called
Leimert Park.
Being Tuesday, it wasn't actually so jazzy - at least not as far
as we could see. But, the catfish was good, as were the black-eyed peas!

Later we went to a great video store called
Cinefile, which specializes
in the most obscure movies. Wanna see a Turkish remake of Star Trek,
or the Wizard of Oz? They've got it! And they've got movies organized by
categories... including some really specialized categories, like
"Big Goofy Monsters" or "Burly Babysitters". We
wound up watching an 1931 Frank Capra comedy called
Platinum Blonde -
only so-so, but fun in its way.

It's the Winter Solstice - the shortest day of the year!
Here in Riverside, the Sun rose at 6:54 am and set at 4:47 pm,
so the day was 9 hours and 53 minutes long. Up in San Francisco,
where I was not long ago, the sun rose at 7:21 am and set at 4:53
pm (hmm - later!), so the day was 9 hours and 46 minutes long.
Just a small difference - I was curious about that.
But it's a lot less cloudy here....

We bought a transformer for the printer Lisa bought in Shanghai -
we got it at a great store called the Electronics Warehouse, located on Main Street north
of downtown Riverside: the part of town where all the really practical
stores are, like auto body shops, machine shops and metal supply
shops. Nowadays Radio Shack tries to makes its money selling cell
phones, and the kids who work there don't know an amp from an ohm. But
at the Electronics Warehouse, the salesman talked to us knowledgeably
and entertainingly for 20 minutes about which wattage transformer to
buy for a laserprinter! By the end, I could draw a graph showing how
much power a laserprinter sucks up from the time you turn it on
to the time it's hot and ready to print.

The place was full of connectors, adaptors, cables and components,
all neatly labelled and displayed. I'll never go to Radio Shack again.

In the morning I
worked with Derek Wise on
a paper we're writing with Jeffrey Morton, Laurent Freidel, and
Aristide Baratin. This paper is about representations of the Poincaré
2-group, a gadget I invented
a while back.
These representations have already been studied by
Crane and Sheppeard,
but there's a lot left to do with them.

In the afternoon I started polishing the version of my
Lectures on Classical Mechanics that
Blair
Smith kindly typeset for me - out of the blue!
I'm hoping this will be the start of a trend. I've got a
lot of lectures that I'd like to turn into
books, but I'll never do it alone. I offered to make Blair a coauthor,
but so far he has modestly refused, even though he wrote a lot of
text when turning Derek Wise's handwritten
notes into a typed manuscript.

As Christmas approaches and thousands of people are stuck in a
blizzard
in Denver Airport, I feel like talking more about ice.

One of the strangest features of North America at the
end of the last Ice Age were the large regions of
"stagnant ice". As the glaciers retreated,
ice became buried by sediments called
glacial till
and wind-borne dust called
loess.
The ice was thick and well insulated, so it lasted for a long time.
For example, in North Dakota there was a 60-kilometer wide zone
of stagnant ice. It started out being as much as 100 meters thick!
It lasted from 10,000 BC to 7,000 BC. The signs of its presence
are still visible now.

The ice in stagnant
ice terrain was for the most part buried
deep, too deep for it to influence the environment on the surface.
But this was not the case everywhere. There were occasional thin
spots or even gaps in the insulating drift blanket, and here the ice
began to melt. It melted in summer sun and dissolved in summer rain.
Meltwater and rainwater together must have formed rivulets that drained
into crevasses and then spread laterally, eroding a network of tunnels
and caverns in previously insulated ice. Even while forest was in the
process of developing over much of the area, the ground was crumbling
here and there, where the stagnant ice had become honeycombed and
weak around the thin spots and where cavern roofs caved in.

At the surface, the scene was one of sudden subsidences of the ground
where the ice had given way beneath. Patches of forest sank into hollows,
drowing the terrestrial plants. Much of the forest was "drunken
forest," with trees leaning in every direction owing to the
instability of the ground. On a small scale, the topography was continually
changing. Sometimes the slumping exposed a cliff of ice, which would begin
to melt as soon as it was exposed to sunlight and air. Innuerable little
superglacial puddles and pools were formed because of the subsidences.
They were icy cold and probably, like glacial lakes today, milky with
rock flour;
as environments for life, they were unpromising.

The continued melting of the ice where it was poorly insulated
improved insulation. The negative feedback process that allowed
melting ice to slow its own melting worked as follows: the ice was
"dirty," with embedded rocks (how dirty is not known),
and as the surface gradually sank lower at the thin spots because of
melting, the rocks were released from their icy matrix and acuumulated.
Thus, in time, the thin spots in the original insulation automatically
repaired themselves, and the melting slowed considerably. The insulation
was also augmented everywhere by wind-borne dust from the zone of
newly exposed land next to the ice sheet margin (which was not
far away to begin with) and by accumulating forest floor litter, humus,
and soil.

[...]

It is known from studies made in Alaska that a drift layer
two meters thick insulates surface lakes from buried ice completely.

Gradually the insulation became absolute. Gradually the terrain
became less active in the sense that slumps and subsidences became less
and less frequent. The melting of the buried ice (which continued
to melt, of course, or it would be there still) came to be caused
entirely by the earth's internal heat. And meltwater from the buried
ice contributed progressively less to the lakes until they were supplied
entirely by precipitation.

[...]

Stagnant ice terrain finally ceased to exist when the last of the
buried ice melted, about 9k B.P. [that is, 9000 years ago, or 7000 BC].
At first, lakes that had been superglacial were led down onto
bedrock, becoming so-called
ice-walled lakes for as long as the surrounding ice remained.
The last blocks to melt left the holes occupied by
modern
prairie
potholes. All the land surfaces gently collapsed, because
of the disappearance of the ice that had supported them. The lowered
land levels allowed the ice-walled lakes to drain, and their sediments,
which had accumulated layer upon layer to a considerable thickness,
were left high and dry as flat-topped hills.

By the end of the
melting period, at about 9k B.P., a reversal of the original topography
had taken place, so that the fossils of lake-dwelling organisms are
found on what are now hill tops.

A low-key Christmas. We opened presents, had breakfast, called my
parents and sister in Virginia, and my aunt in Pasadena. I wrote
This Week's Finds while Lisa
copied the instructions for several tai chi forms from
VCDs to MP3s.

We had homemade pizza for dinner - a kind of tradition I haven't
engaged in for months, since only Lisa has
the energy to make the crust from scratch, though it's easy with a
bread machine. And, we watched the first two episodes of Star Trek:
The Next Generation. Lisa bought DVDs of the entire show in Shanghai -
it'll be fun to see the whole thing in order, without commercials.

The Bush administration is considering listing the polar
bear as a threatened species. As the Arctic melts,
polar bears are starving and drowning as they need to swim longer
and longer distances between ice floes. There are even reports of
cannibalism. There are between 20,000 and
25,000 polar bears in the world, with about 4,700 in Alaska. Their
population has declined about 20% since 1990.

The polar bear would be the first animal to be listed as threatened
due to global warming. If it's listed, this would
require government agencies to take no action that threaten it further.
But, the Bush administration has said there would be no new curbs on
oil drilling in Alaska or limits on greenhouse gas emissions.

Now that everyone is talking about Ethiopia's war against the
Islamic
Courts Union in
Somalia, I can't
resist pointing out that I discussed the Islamic Courts Unions
June
13th. These news stories start as tiny newspaper items
and then blossom "all of a sudden" into public visibility.
If my diary often seems alarmist, it's because I like
to spot worrisome trends while they're still small.
I'm not sure why - it's not as if I'm actually able to do
anything about most of these trends. I just like to "stay on
top of things".

Having spent the summer in China, heavily reliant on broadband
internet to feel connected to the world, this story fascinates and
appalls me:

Another devastating Boxing Day earthquake exposes the lack of infrastructure
depth in Asia

At this point nobody seems to know how long it will take to restore normal
service. Estimates go as long as three weeks. Verizon, the international
communications giant which is responsible for some of the cables, said it
could take as long as five days to even get a cable ship into the earthquake
region. The cables themselves are at about 3,400 meters below the ocean
floor, meaning submersibles can't get to them. Surface ships must search for
them with grappling hooks on a muddy and disrupted sea bed, then pull them
up to repair them.

For publications like Asia Sentinel and many others, which exist only online,
the effect has meant a flat inability to operate. Hong Kong has only a single
Internet gateway coming into the territory, meaning that the attempt to
squeeze vast amounts of information through it has resulted in long delays.
Bankers complained to the media that they were unable to execute trades
because of their inability to secure verbal approval from overseas clients.
Most dealing rooms were trading lightly because of the Christmas holidays.
Nonetheless, bond and equity traders, who depend on the flow of real-time
data, said they were hampered by the disruptions.

[...]

The cables handle traffic between China, Japan, Korea, Southeast Asia, the
US and Taiwan. Taiwan lost almost all of its ability to communicate by
telephone to Japan. Some 90 percent of capacity to Southeast Asia was
wiped out. Two days later, Hong Kong was still largely without Internet
service, leaving those with a vital need for the web with no ability to
communicate. PCCW, the territory's primary Internet service provider,
said data capacity had been cut in half. In China, according to China
Telecom Corp., the mainland's largest fixed-line carrier, 97 percent of
mainland Internet users had difficulty accessing overseas websites, and
57 percent said their lives and work had been affected.

While the largest amount of communications infrastructure goes through
Taiwan a second set of lines goes out of Singapore, through Australia
and on to the US. That set of lines is still up, but it was quickly
overwhelmed by the amount of traffic switched to it.

Because everybody is competing for the available bandwidth, there is
congestion now on the remaining bandwidth - a Singapore telecommunications
spokesman told a local newspaper.

Ironically, inside China itself, domestic traffic is largely unaffected,
since it is a domestic system closely guarded by authorities. Given China's
closely monitored information system, there is no international access to
the outside world.

Internationally, it was another case. The Internet Traffic Report, a website
reporting on worldwide Internet use, reported that "packet loss",
the discarding of data packets in a network when a device is overloaded and
cannot accept incoming data, was still total in Shanghai two days after the
earthquake. Indonesia was running at 50 percent and Singapore at 75 percent.
Like China, Taiwan was unable to receive any data from outside the country.

A National Public Radio reporter in Shanghai did a
story on this disaster which contains an
interesting nugget of information. The Chinese government has
recently blocked the NPR website! When Lisa and I were in Shanghai,
we listened to National Public Radio news on the computer every morning.

I did, however, notice a lot of censorship of the world-wide web
in China. The Wikipedia was completely blocked -
but as the Wikipedia itself points out, "Technically adept
Internet users in China are currently able to circumvent the block
fairly easily."

The BBC and Voice of America were also blocked.
And, any webpage mentioning the phrase
"h-m-n r-ghts" was blocked. Now I read that
"T--w-n ind-p-----ce" is also forbidden.

(Can someone in China let me know if they see this diary page, after
the internet is working again?)

But, to my surprise, ABC, CBS, NBC and National
Public Radio were completely accessible!

In many cases I could see the existence of blocked webpages
via Google - but if I tried to click on them, I'd get an error message.
Sometimes this would disable Google for a while afterwards... I never
could quite figure out the pattern. At times I got scared that I'd
hear a knock on my door. But, I figured they weren't mainly worried
about Americans reading English-language websites.

This afternoon, Lisa and I got a marriage license at the
Riverside county clerk! We'll get married pretty soon....

A 41-square-mile shelf of floating ice that jutted into the Arctic
Ocean for 3,000 years from Canada's northernmost shore broke away
abruptly in the summer of 2005, apparently freed by sharply warming
temperatures and jostling wind and waves, scientists said yesterday.

The Ayles ice shelf, as the ancient 100-foot-thick slab was called,
drifted out of a fjord along the north coast of Ellesmere Island when
the jumbled sheath of floating sea ice that tended to press against
the coast there even in summers was replaced by open waters because of
the warming, the scientists said.

The change was first noticed by Laurie Weir of the Canadian Ice
Service as she examined satellite images taken of Ellesmere and
surrounding ice on and after Aug. 13, 2005. In less than an hour,
around midday that day, a broad crack opened and the ice shelf was on
its way out to sea.

The shelf is one of the few remnants of a broad expanse of floating
shelves of ice that once protruded along much of the Ellesmere coast,
somewhat like the brim on a hat.

Such shelves are far thicker and older than the milling cloak of sea
ice that drifts atop the Arctic Ocean. The sea ice consists of floes
ranging from 3 to 9 feet thick or so that are built up over just a few
years.

The Arctic sea ice has experienced sharp summertime retreats for
several decades, adding to evidence of significant warming near the
North Pole. (Neither melting ice shelves nor sea ice contribute to
rising sea levels because they sit in the sea already, like ice cubes
in a drink.)

Ninety percent of the 3,900 square miles of ice shelves that existed
in 1906 when the Arctic explorer Robert Peary first surveyed the
region are gone, said Luke Copland, the director of the University of
Ottawa.s Laboratory for Cryospheric Research.

In a paper summarizing the event but not yet published, Dr. Copland
and other researchers said that the transformation of the Ayles ice
from a shorebound shelf to a drifting ice island appeared to be a
result of unusual Arctic warmth in 2005 on top of a longer-term
warming trend.

All this is small potatoes compared with Iceberg
B-15, the largest known iceberg on record, which peeled off
the Ross Ice Shelf of
Antarctica in March 2000.
According to the
Iceberg FAQ,
it was about 300 km × 27 km in area
and roughly 500 meters thick.

Our friend Lothar just came back from a trip to
Germany and Israel - but on New Year's Even, he had to catch a flight
to Hong Kong at midnight! So, we drove in to LA to have an early
dinner with him, along with Chris and Menakshee. Then we drove back,
getting home at 11. Chris and Menakshee drove him to the airport
(since all the cabs were busy) and caught up with us just in time to celebrate
the New Year. They spent the night at our house and then went to
Joshua Tree.

Lothar has a huge library - mainly about China. All his walls
are lined with books, and he's constantly needing to buy new bookshelves.
I grabbed ahold of this one, and liked it better than I expected:

The I Ching
is an ancient Chinese text, dating back to the
time when dates get very fuzzy - sometime between 1000 and 3000 BC,
let's say. It describes the meaning of the 64
hexagrams - basically,
strings of 6 bits, like this:

In these hexagrams, a solid line
stands for yang (presence, positivity), while a broken line
stands for yin (absence, negativity). As this famous symbol indicates:

yin and yang lead to each other in an endless round (as shown by the
swirly pattern), and interpenetrate each other (as shown by the little dots).

The hexagrams correspond to complex mixtures of yin and yang, and
each one has its own complicated personality. They're each built from
two
trigrams.
For example, the one I just showed you:

is called "Dispersal" - it's the trigram for "wind"

on the trigram for "water":

Leibniz got the idea of binary digits from the hexagrams!
The idea that everything is built up from a simple binary opposition
is very appealing, though of course the ancient Chinese weren't able to
make it scientific in the modern sense.

One thing I like about Wilhelm's book
is the detailed discussion of the 8 trigrams. They make some
sense if you know how the system works and are willing to engage in a
bit of free-wheeling magical thinking. For example, the completely
positive trigram:

stands for "heaven" or "sky", while the completely
negative one stands for "earth".

Most people are aware that half of North America was once covered
by an ice sheet kilometers thick, and they marvel at the contrast
between conditions then and now. Not nearly so many try to visualize
the remarkable scenery of intervening times while the ice was in
the process of melting. - Evelyn C. Pielou